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This is a Medium difficulty Coding & Algorithms question, commonly asked during Onsite rounds at Motive.

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This question is commonly asked for Software Engineer candidates at Motive during technical interviews.

Implement Union-Find and track components

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding and implementation of the Disjoint Set Union (Union-Find) data structure, covering union by rank, path compression, API design for union(a, b), connected(a, b), count(), and analysis of time and space complexity.

Motive

Sep 6, 2025, 12:00 AM

Software Engineer

Onsite

Coding & Algorithms

Implement a Disjoint Set Union (Union-Find) data structure with union by rank and path compression. Design the API to support union(a, b), connected(a, b), and count() for the number of connected components. Given n nodes (0..n-

and a stream of operations, return the result of each connected query and the component count after each union. Analyze time and space complexity and discuss thread-safety considerations.

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